Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent. It models growth or decay processes.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant b in the function f(x) = a * b^x. It determines the rate of growth (b > 1) or decay (0 < b < 1).

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * e^(-kx), where a is the initial amount, k is a positive constant, and e is Euler's number (approximately 2.718).

Tags

CCSS.HSF-IF.C.8B

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1 (b > 1), while exponential decay occurs when the base is between 0 and 1 (0 < b < 1).

Tags

CCSS.HSF-IF.C.8B

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, expressed as f(x) = log_b(x), where b is the base. It answers the question: to what exponent must the base b be raised to produce x?

Front

What is the natural logarithm?

Back

The natural logarithm is a logarithm with base e (approximately 2.718), denoted as ln(x). It is commonly used in calculus and exponential growth/decay problems.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function f(x) = a * b^x is the line y = 0, which the graph approaches as x approaches negative infinity.

Tags

CCSS.HSF-IF.C.7E

Front

How do you find the equation of a horizontal asymptote?

Back

To find the equation of a horizontal asymptote for a function, identify the value that the function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is the compound interest formula?

Back

The compound interest formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

How do you model exponential growth in real-life situations?

Back

Exponential growth can be modeled using the function f(t) = A_0 * e^(rt), where A_0 is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-LE.A.1A